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Abstract

Multi-state Markov models are widely used for prediction in reliability, safety, and risk analysis. Systems typically pass through different states between correct, reliable operation and failure, as a result of external events or internal ageing, and Markov models provide an effective compromise between realism and mathematical tractability. Statistical flowgraphs analyse these models using transforms of the transition time distributions between states, which are combined and inverted to obtain quantities of interest for the entire model. This paper presents an approach to flowgraphs using empirical transforms based on historical or testing data, with no assumption of parametric probability models for transition times. The non-parametric method is illustrated with an application to predicting cumulative earthquake damage to structures.

Keywords

multi-state model Markov chain semi-Markov process Poisson process cumulative damage seismic event earthquake

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System reliability and safety assessment using non-parametric flowgraph models

Abstract

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